Theorem 2.1 \((\) Corollary 11.2 [1]}\()\) 
Let \(\mathfrak {C}\)  be a closed convex set in a Banach space \(\mathfrak {B}\)  and let \(\mathcal { L}\)  be a continuous mapping of \(\mathfrak {C}\)  into itself such that
the image \(\mathcal { L}\mathfrak {C}\)  is precompact. Then \(\mathcal { L}\)  has a fixed point.

